Fair correction on the altitude (still in the lower bounds of the balloons, as I mentioned).
The SR-71 already flew in the configuration I mentioned. It's the YF-12C (a converted SR-71).
Recovering and converting another sure is more expensive than one missile, but it's a reusable platform.
A ground missile able to reach those balloons is more expensive than a modernized SR-71 sortie. High-altitude, precision missiles are also not allocated for this task. China can launch dozens of balloons for cheap, and spending one multi-million-dollar missile on each is insanity. Even the long range air-to-air ones are too expensive for that.
The SR-71 (as a new YF-12D interceptor) makes more sense. It can take multiple balloons in one flight with cheap shorter range air-to-air missiles (or maybe even cheaper weapons, for a balloon a laser would do), then go home and do that over and over again.